Question

\(P=\left(\frac{1}{4.9}+\frac{1}{9.14}+\frac{1}{14.19}+...\frac{1}{44.49}\right)\frac{1-3-5-7-...-49}{89}\)

Thực hiện phép tính trên, viết cách giải rõ ràng, dễ hiểu

Answer 1

Đặt \(A=\frac{1}{4.9}+\frac{1}{9.14}+...+\frac{1}{44.49}\)

\(5A=\frac{1}{4}-\frac{1}{9}+\frac{1}{9}-\frac{1}{14}+...+\frac{1}{44}-\frac{1}{49}\)

\(5A=\frac{1}{4}-\frac{1}{49}\)

\(A=\frac{45}{196}:5=\frac{9}{196}\)

Đặt \(B=\frac{1-3-...-49}{89}\)

\(B=\frac{\left(1-3\right)-\left(5-7\right)-...-\left(47-49\right)}{89}\)

\(B=\frac{\left(-2\right)-\left(-2\right)-...-\left(-2\right)}{89}\)

\(B=\frac{-2+2+...+2}{89}\)

\(B=\frac{\left(-2\right)+2\times24}{89}\)

\(B=\frac{46}{89}\)

\(P=A.B=\frac{9}{196}.\frac{46}{89}\)

\(P=\frac{207}{8722}\)